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Re: Re: When is a List not a List?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg90986] Re: [mg90956] Re: [mg90947] When is a List not a List?
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Sat, 2 Aug 2008 03:25:19 -0400 (EDT)
  • References: <200807310656.CAA07700@smc.vnet.net> <16711231.1217501820078.JavaMail.root@m08> <op.ue54zeqq2c6ksp@bobbys-imac> <21465667.1217530845998.JavaMail.root@m08> <op.ue6m0tdk2c6ksp@bobbys-imac> <32926975.1217563920588.JavaMail.root@m08> <op.ue7o67wi2c6ksp@bobbys-imac>

Because there are lots of plots of the kind which I just sent  
(Plot[x /. Solve[x^3 - 3 x^2 + a == 0, x], {a, -3, 5}]) but where you  
have FindRoot or NMaximize etc., instead of Solve and the first  
argument can't be evaluated until the value of the parameter a has  
been supplied. There have been lots of post of this kind on this forum  
so its kind if weird you managed to miss them all.

Andrzej Kozlowski




On 1 Aug 2008, at 16:29, DrMajorBob wrote:

> Agreed.
>
> And I'm wondering what advantage HoldAll has, in the case of Plot,  
> since a plot can't result without evaluating the arguments?
>
> Why NOT evaluate the first argument, at least, before making style  
> decisions/assignments?
>
> The defense that "everybody already knows this" is irrelevant to the  
> question of how we'd LIKE Plot to behave.
>
> Naturally, we won't necessarily GET what we want... but we're  
> entitled to say what that is.
>
> I'm trying to think how David Park's Presentations package handles  
> such things.
>
> Bobby
>
> On Thu, 31 Jul 2008 22:33:50 -0500, AES <siegman at stanford.edu> wrote:
>
>> At 7:44 PM -0500 7/31/08, DrMajorBob wrote:
>>> Plot COULD assign colors after evaluation, OTOH... the fact that  
>>> it doesn't is a design choice/artifact, not a necessity  
>>> preordained by fate.
>>>
>>> That being so, users are entitled to find it odd at first glance.  
>>> (Or even second... maybe third.)
>>
>> If the above is true -- and I'd suppose it is -- then I'd say it's  
>> also very much an unfortunate, not to say flat-out *bad* design  
>> choice or artifact.
>>
>> An innocent novice-level user creates a Plot[ ] with three curves  
>> using the {f1, f2, f3} List form of the first argument, and  
>> discovers that M by default assigns a different color to each curve  
>> -- a good and helpful default design choice on M's part, I'd say.
>>
>> Maybe this novice user wants to go a bit further: Thicken certain  
>> curves, change the Dashing, and so on.  He or she discovers the  
>> PlotStyle option (or equivalent); learns how to do this; is happy.
>>
>> And then this user also realizes: Hey, I could plot 8 or 10 curves  
>> this way, without having to type in f1 thru f8 by just using a  
>> Table[ ] command for the first argument and iterating over some  
>> appropriate parameter.  A Table[ ] creates a List, right?
>>
>> So he/she does this; the 8 or 10 curves appear exactly as desired;  
>> except the styling behavior is suddenly all screwed up.  Once  
>> again, a classic M-style Gotcha!!! -- and a particularly nasty  
>> Gotcha:  Am I getting this unwanted result because of the way I  
>> structured the PlotStyle commands I used? -- or because of  
>> something mysterious with using Table[ ]?  The coloring and so on  
>> in the default  {f1, f2, f3} case has the nice default cycling  
>> behavior for the styling -- Why am I not getting it now?
>>
>> Andrzej says this unfortunate result _has_ to be the case because  
>> Plot[ ]  doesn't "pre-Evaluate" the first argument.
>>
>> Well, somehow, if the first argument is {f1, f2, f3, f4, f5, f6,  
>> f7, f8}, Plot[ ] somehow "pre-evaluates" (lower-case pre-evaluate)  
>> this argument at least enough to know that it's not only a List,  
>> but how many elements that List has.  Is it somehow impossible for  
>> Plot[ ] to know that Table will also produce a List, and to  
>> similarly pre-evaluate how many elements that List will have?  I  
>> suspect it's not impossible.
>>
>> And if that is indeed impossible with the PlotStyle option in  
>> Plot[ ] then can Andrzej  explain how it _is _ possible for Plot[ ]  
>> to somehow handle the PlotRange->All option correctly (i.e.,  
>> identically) with either form of the first argument -- even though  
>> that option needs to determine not only the number of curves in the  
>> first argument, but the maximum and minimum values over all those  
>> curves, in order to set the axes and axis Tick locations and values  
>> for the plot.  Is just getting the number of curves and picking the  
>> colors for them really harder than that?
>>
>> I very much like DrMajorBob's wording here:  I'll bet the coloring  
>> problem with List vs Table is precisely "an [accidental] design  
>> choice/artifact, not a necessity preordained by fate" -- and an  
>> unfortunately unfortunate "design choice/artifact".
>>
>> The only things more unfortunate are (a) that M has a fair (and  
>> increasing?) number of these Gotchas; (b) M's documentation is  
>> substantially less helpful than it could or should be either in  
>> diagnosing or in warning about them; and (c) it's far from clear  
>> that anyone at WRI really recognizes these points.
>>
>>
>>
>>
>
>
>
> -- 
> DrMajorBob at longhorns.com



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